A twisted theorem of Chebotarev

TL;DR

This paper extends Chebotarev's density theorem to the setting of difference algebraic geometry over function fields, utilizing Galois coverings and Hrushovski's twisted Lang-Weil estimate.

Contribution

It introduces Galois coverings of difference schemes and applies Hrushovski's estimate to prove a function-field version of Chebotarev's theorem.

Findings

Established a function-field Chebotarev density theorem in difference algebraic geometry

Developed the concept of Galois coverings for difference schemes

Applied twisted Lang-Weil estimates to this new setting

Abstract

We prove a function-field version of Chebotarev's density theorem in the framework of difference algebraic geometry by developing the notion of Galois coverings of generalised difference schemes, and using Hrushovski's twisted Lang-Weil estimate.